Problem: What's the first wrong statement in the proof below that $ \triangle BCA \cong \triangle BCE$ $ \; ?$ $ \overline{BC} $ is parallel to $ \overline{DF} $. This diagram is not drawn to scale. $A$ $B$ $C$ $D$ $E$ $F$ Givens $ \angle BED \cong \angle BAC$ $, \ $ $ \overline{DE} \cong \overline{AC}$ $, \ $ $ \angle BDE \cong \angle ACB$ $, \ $ $ \overline{EF} \cong \overline{AB}$ $, \ $ $ \angle CEF \cong \angle BAC$ $, \ $ and $\ $ $ \angle ECF \cong \angle ACB$ Proof $ \triangle BCA \cong \triangle BDE$ because ASA $ \angle CFE \cong \angle BAC$ because alternate interior angles are equal $ \overline{AB} \cong \overline{BE}$ because corresponding parts of congruent triangles are congruent $ \triangle FCE \cong \triangle BCA$ because AAS $ \overline{AC} \cong \overline{CE}$ because corresponding parts of congruent triangles are congruent $ \triangle BCA \cong \triangle BCE$ because SSS
Explanation: Try going through the proof yourself: write down the givens, and then see if they justify the next step for the reason given. Then do the same thing for the next step, and the next, until you run into something that you can't justify, or you finish the proof. $ \angle BAC \cong \angle CFE$ is the first wrong statement.